# -*- coding:utf-8 -*-


#
# Suppose you have N integers from 1 to N. We define a beautiful arrangement as an array that is constructed by these N numbers successfully if one of the following is true for the ith position (1 <= i <= N) in this array:
#
# The number at the ith position is divisible by i.
# i is divisible by the number at the ith position.
#
#
#
#
# Now given N, how many beautiful arrangements can you construct?
#
#
# Example 1:
#
# Input: 2
# Output: 2
# Explanation: 
# The first beautiful arrangement is [1, 2]:
# Number at the 1st position (i=1) is 1, and 1 is divisible by i (i=1).
# Number at the 2nd position (i=2) is 2, and 2 is divisible by i (i=2).
# The second beautiful arrangement is [2, 1]:
# Number at the 1st position (i=1) is 2, and 2 is divisible by i (i=1).
# Number at the 2nd position (i=2) is 1, and i (i=2) is divisible by 1.
#
#
#
# Note:
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# N is a positive integer and will not exceed 15.
#
#


cache = {}
class Solution(object):
    def countArrangement(self, N):
        def helper(i, X):
            if i == 1:
                return 1
            key = i, X
            if key in cache:
                return cache[key]
            total = sum(helper(i - 1, X[:j] + X[j + 1:])
                        for j, x in enumerate(X)
                        if x % i == 0 or i % x == 0)
            cache[key] = total
            return total
        return helper(N, tuple(range(1, N + 1)))
